This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and

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2 Tectonophysics 587 (2013) Contents lists available at SciVerse ScienceDirect Tectonophysics journal homepage: The effect of microstructural and rheological heterogeneity on porphyroblast kinematics and bulk strength in porphyroblastic schists Ben M. Frieman, Christopher C. Gerbi, Scott E. Johnson University of Maine, School of Earth and Climate Sciences, Bryand Global Sciences Center, Orono, ME , USA article info abstract Article history: Received 5 May 2012 Received in revised form 31 October 2012 Accepted 7 November 2012 Available online 20 November 2012 Keywords: Staurolite boudinage Porphyroblast rotation Viscous strength Microstructure Strain partitioning Vorticity The kinematic record and bulk viscous strength of polyphase rocks depend in part upon the relative strengths and distributions of rheologically distinct fabric elements. Here, we explore the effects of microstructural and rheological heterogeneity in porphyroblastic schists. Electron backscatter diffraction and petrographic analyses reveal asymmetric microboudinage of staurolite, indicating relative rotation of staurolite porphyroblasts synchronous with bulk non-coaxial strain. Boudinage and relative rotation both require porphyroblast matrix shear coupling. Based on 2D optical observations, the extent of the coupling appears related to the initial and boudinaged staurolite grain shape and orientation as well as the geometry of heterogeneities such as mica domains or shear bands. We designed 2D finite element numerical models to assess the role of microstructural variation and rheological heterogeneity on the degree of porphyroblast matrix shear coupling and bulk viscous strength. Model results indicate that the bulk strength of a three-phase system comprising inclusion, weak domain, and matrix is sensitive to the relative proximity of weak and strong domains, particularly at high viscosity contrasts (i.e. η matrix /η weak >10). The threshold for bulk weakening below the matrix strength occurs over a narrow range of weak domain viscosities (η matrix /η weak = ), regardless of the relative abundance and spatial distribution of weak domains. Kinematic decoupling of porphyroblasts occurs at low viscosity contrasts when weak domains are proximal (η matrix /η weak =2 5), but for all other spatial distributions and modal abundances investigated, kinematic decoupling occurs at viscosity contrasts of η matrix /η weak = These data indicate that bulk weakening due to rheological heterogeneity is not necessarily coincident with kinematic decoupling Elsevier B.V. All rights reserved. 1. Introduction To unravel the kinematics and dynamics of orogens, we rely in large part on the microstructural record. Tim Bell has made seminal contributions to our understanding of porphyroblast microstructures in the orogenic context, and we take the opportunity of this special volume to address the issue of porphyroblast kinematics and the use of microstructural modeling to infer the bulk strength of rocks. Due to their ability to preserve multiple deformation events and metamorphic conditions, porphyroblastic schists provide rich opportunities for reconstructions of past and changing deformation environments. However, one challenge associated with these rocks is that mineral-scale information, such as phase distribution and porphyroblast inclusion trail geometry, does not always predictably relate to macroscale kinematics and bulk properties such as strength Corresponding author at: Colorado School of Mines, Department of Geology and Geological Engineering, 1516 Illinois Street, Golden, CO 80401, USA. Tel.: ; fax: addresses: bfrieman@mines.edu (B.M. Frieman), christopher.gerbi@maine.edu (C.C. Gerbi), johnsons@maine.edu (S.E. Johnson). (e.g., Fossen and Tikoff, 1993; Jiang, 1994a,b; Jiang and Williams, 2004; Johnson, 2008; Johnson et al., 2009a,b; Lister and Williams, 1983). For example, due to strain partitioning, the kinematic vorticity number as recorded by a population of porphyroblasts may not reflect the bulk strain field (e.g., Bailey and Eyster, 2003; Jessup et al., 2006; Johnson et al., 2009a,b; Klepeis et al., 1999; Law et al., 2004; Thigpen et al., 2010; Wallis et al., 1993; Xypolias and Koukouvelas, 2001). Comparatively, growth of effectively rigid porphyroblasts can strengthen a rock (e.g., Groome and Johnson, 2006), but well lubricated porphyroblast boundaries may counteract that effect and allow for bulk weakening (e.g., Johnson et al., 2009b). In this contribution, we focus on how the distribution and strength contrast of matrix domains (e.g., mica-rich and mica-poor) can affect porphyroblast rotation and bulk viscous strength. This work serves in part as further evidence that porphyroblasts rotate relative to each other, but more importantly to identify the conditions under which (1) interpretations of parameters such as kinematic vorticity number derived from grain or inclusion-trail orientations are valid and (2) porphyroblast growth strengthens a rock. Both the bulk strength and the relationship between porphyroblast kinematics and bulk kinematics depend strongly on the distribution and strength contrast of rheologically distinct matrix /$ see front matter 2012 Elsevier B.V. All rights reserved.

3 64 B.M. Frieman et al. / Tectonophysics 587 (2013) elements. To demonstrate this, we use a well-preserved kinematic record of microboudinaged staurolite porphyroblasts in a schistose matrix and finite element numerical modeling of analogous synthetic microstructures. 2. Kinematic vorticity measurements and controls on bulk strength Many methods exist for evaluating the rotational component of strain, including the crystallographic or shape preferred orientations of rigid objects and their internal inclusion fabrics (e.g., Holcombe and Little, 2001; Johnson et al., 2009a,b; Masuda et al., 1995; Passchier, 1987; Simpson and DePaor, 1993, 1997; Wallis et al., 1993), crystallographic and shape preferred orientations in the matrix (Johnson et al., 2009a,b; Law, 2010; Passchier, 1987; Sullivan, 2008; Vissers, 1989; Wallis, 1993, 1995; Wenk et al., 1987; Xypolias and Koukouvelas, 2001), and deformed veins or dykes (Kuiper and Jiang, 2010; Passchier and Urai, 1988; Short and Johnson, 2006; Wallis, 1992). Application of the rigid clast method requires several assumptions, including measurements from a plane orthogonal to the rotation axis of the clast, ideal clast matrix shear stress coupling, Newtonian viscous matrix behavior, clast shapes approximated as ellipsoids, clast shapes which do not change during deformation due to recrystallization or fracturing, sufficiently large strains such that clasts attain stable sink positions, no mechanical interaction among clasts, lack of strain partitioning at clast matrix interfaces due to lubrication by a low viscosity material, and steady state, homogeneous bulk flow conditions at the scale of measurement (Jeffery, 1922; Johnson et al., 2009a,b; Means et al., 1980; Passchier, 1987; Passchier and Trouw, 2005; Xypolias, 2010 and reference therein). Because all these assumptions are rarely satisfied, the rigid clast method can substantially underestimate the kinematic vorticity number (e.g., Bailey and Eyster, 2003; Jessup et al., 2006; Johnson et al., 2009a,b; Klepeis et al., 1999; Law et al., 2004; Thigpen et al., 2010; Wallis et al., 1993; Xypolias and Koukouvelas, 2001). In direct contrast to the interpretation of clast rotation, some workers, citing partitioning of kinematic parameters, have asserted that porphyroblasts (i.e. rigid clasts) remain confined to zones of pure shear and therefore do not rotate relative to one another or an external reference frame during non-coaxial deformation events (Bell, 1985; Bell and Hayward, 1991; Bell et al., 1992). In this interpretation porphyroblasts and their internal inclusion fabrics can be used to reconstruct the geometric evolution of complexly deformed metamorphic terranes (e.g., Bell and Newman, 2006; Bell et al., 1995; Cihan et al., 2006; Sanislav and Bell, 2011; Yeh, 2007). The primary difference between these two end-member applications of porphyroblasts is the degree of porphyroblast matrix coupling, which is affected by strain partitioning and the distribution of weak and strong minerals (e.g., Bell, 1981, 1985). To assess the relevancy of these end-member applications it is first necessary to establish porphyroblast matrix shear coupling relationships. This may be done by constraining porphyroblast rotation synchronous with grain growth (e.g., Busa and Gray, 2005) or by constraining differential rotation of whole grains or grain fragments during shear that postdates porphyroblast growth (e.g., Hippertt, 1993; Johnson et al., 2006; Mezger, 2010; this study). Therefore, the timing of grain growth is less pertinent than the rheological and microstructural configuration that is coeval with non-coaxial deformation, which can significantly influence the partitioning of strain, degree of porphyroblast matrix shear coupling, and thus the rotational behavior of rigid porphyroblasts. The bulk strength of a polycrystalline material depends on three main factors: the strength contrast among the constituent phases, their modal abundance, and their spatial distribution. At the extreme, isolated spherical weak phases in a strong matrix provide an upper strength bound for a given mode and strength contrast (cf. Voigt, 1928), whereas layered weak phases provide a lower strength bound (cf. Reuss, 1929). Geological materials do not approach these bounds, but the distribution and degree of weak phase interconnection can exert significant control on the bulk strength (e.g., Gerbi, 2012; Handy, 1994; Holyoke and Tullis, 2006). Little is known about how rheological heterogeneities that affect bulk strength relate to those that affect porphyroblast matrix coupling. 3. Geologic setting The samples presented in this study are from the Appleton Ridge Formation, located in south-central Maine, USA (UTM: E N, 19T). This region experienced a protracted history of Silurian Devonian orogenesis coincident with extensive plutonism, ductile deformation, and metamorphism (Bradley et al., 2000; Guidotti, 1989; Stewart et al., 1995; Tucker et al., 2001) due to the collision of multiple island arc systems, microcontinents, and proximal sedimentary basins with differing tectonic affinities (Fig. 1; see Murphy and Keppie, 2005; Tucker et al., 2001; van Staal et al., 1998; van Staal et al., 2007 for detailed tectonic syntheses). Regional deformation resulted in a series of overprinting structural fabrics including a poorly recognized D 1 event associated with recumbent isoclinal folds and inferred overturned stratigraphy as well as a strong D 2 fabric that is characterized by upright to overturned tight and open folds that locally display a well developed axial planar cleavage and control general map patterns in the region (Fig. 1B; Hussey, 1988). The present dominant fabric (S 3 ) is a reactivated foliation that is subparallel to the earlier formed axial planar foliation (S 2 ) and is associated with the development of dextral asymmetric folds. The study area exhibits ubiquitous outcrop to microscale asymmetric dextral shear structures including asymmetric boudinage, north trending asymmetric folds (F 3 ), and shear bands (Gerbi and West, 2007; West and Hubbard, 1997). The structures are heterogeneously distributed and consistently display a dextral shear sense across a wide zone (>25 km perpendicular to orogen strike) that affect all lithologies in the study region (Fig. 1B; West and Hubbard, 1997; West et al., 2003). This phase of deformation is inferred, from regional structural analysis and thermochronology, to be the result of diffuse dextral ductile transpression in the middle crust associated with plate reorganization prior to localization associated with the development of the subvertical, right-lateral Norumbega Fault system (West and Hubbard, 1997). Due to this protracted history and across-strike strain partitioning, regional estimates of the mean kinematic vorticity number (W m ) range from W m =0.67 to 0.97 (Johnson et al., 2009a; Short and Johnson, 2006; respectively), reflecting deformation in a long lived zone of oblique convergence. Peak metamorphic conditions reached low to intermediate amphibolite facies and spanned the andalusite and sillimanite stability fields (Bickel, 1976; Guidotti, 1989). Regional work indicates multiple discrete and/or overlapping Late Silurian Devonian amphibolite facies metamorphic events occurred (Gerbi and West, 2007; Guidotti, 1989; West et al., 1995, 2003). 4. Microstructural analysis 4.1. Sample descriptions At the study locality (star in Fig. 1B), the Appleton Ridge Formation is a staurolite andalusite schist interbedded with micaceous quartzites. Beds are typically 5 60 cm and 3 8 cm thick, respectively, and where the quartzite is absent the schist is either bedded or massive (Bickel, 1976; this study). Outcrop-scale dextral shear structures consistent with regional deformation are ubiquitous and include asymmetric boudinage of more competent layers such as pegmatite pods (Fig. 2B) or quartz veins/pods (Fig. 2C,D), asymmetric folds with north trending axial traces (Fig. 2C), and shear bands which deflect the foliation at a low angle and strike (Price et al.,

4 B.M. Frieman et al. / Tectonophysics 587 (2013) Fig. 1. (A) Generalized lithotectonic map of the Northern Appalachians; arrow marks the location of B. (B) Geologic setting of the study area (star); after Hibbard et al. (2006) and Gerbi and West (2007). All faults except the Sennebec Pond fault likely originated as shear zones. NFS = Norumbega fault system. 2010). Outcrops display a well developed subvertical northeast striking foliation (S 3 ) containing a subhorizontal lineation defined by aligned grains of biotite, muscovite, and elongated quartz (Fig. 2A). Present compositional layering probably formed by transposition and accompanying recrystallization. In the schistose layers, porphyroblasts include staurolite, andalusite, garnet, and biotite whereas the matrix comprises quartz, biotite, muscovite, and plagioclase. High local concentrations (>90%) of biotite and/or muscovite grains define a well developed spaced schistosity. This schistosity, which may be discontinuous in thin section, is strongly perturbed by and wraps staurolite, andalusite, and garnet porphyroblasts. The intervening matrix (i.e. microlithons) displays a largely continuous schistosity produced by diffuse biotite (~20 40%) and elongate individual or aggregate grains of quartz and feldspar, which exhibit a shape preferred orientation that parallels the spaced schistosity. Matrix quartz grains generally lack undulatory extinction or subgrains, and preliminary analysis of matrix quartz indicates there is a very weak crystallographic preferred orientation. The transition between the spaced schistosity and the intervening matrix is typically gradational. Staurolite is relatively abundant (5 15% mode), forms large (>1 cm) euhedral to sub-euhedral poikiloblastic grains, and commonly forms symmetrical penetrative twins (60 or 90 inter twin relationship) (Fig. 2E, F). Several populations of similarly oriented twinned staurolites exist at this study site. Staurolite specimens are frequently observed to have: (1) one or both of the twinned limbs at high angles to the foliation and/or the lineation, (2) the long axis of both twinned limbs approximately parallel to the foliation while oblique to the lineation, or (3) no twinning relationship or a relatively simple crystal shape. Evidence for porphyroblast interactions, such as grain tiling or stacking, are common and are generally associated with high local concentrations of staurolite (Fig. 2E). Staurolite crystals preserve internal inclusion fabrics (S i ) which are commonly composed of quartz, feldspar, and illmenite. Inclusions of these minerals define a wide variety of internal fabrics such as straight to slightly curved (Fig. 3A, B, C, and D), microfold crenulations, and less commonly spiral or sigmoidal patterns. Inclusion textures rarely show continuity with the external matrix fabric (S e ) and in many cases planar inclusion textures lie at high angles to the external matrix fabric (Fig. 3B). Many of the aforementioned internal fabrics are present in a

5 66 B.M. Frieman et al. / Tectonophysics 587 (2013) Fig. 2. Annotated field photographs displaying general outcrop scale features of the study area. (A) Outcrop view of porphyroblastic schists interbedded with thin psammitic layers that are largely planar in outcrop (photo courtesy of D.P. West). (B) Asymmetrically sheared pegmatite pod displaying a dextral shear sense; the hammer is 40 cm in length. (C) Asymmetrically folded and sheared quartz vein; the hammer is 40 cm in length. (D) Quartz pod bearing large andalusite crystals and displaying a dextral shear sense; field book is 12 cm from top to bottom. (E) High local concentrations (white arrows), asymmetrical microboudinage (circled areas), and tiling (black arrows) of staurolites porphyroblasts; photo is roughly perpendicular to the foliation. (F) Foliation surface displaying no clear alignment of staurolite porphyroblasts, but several with asymmetrical boudinage of twinned crystals (circled areas); shear is in plane of photograph, photo direction to the south-east. single thin section and differing textures are commonly observed among adjacent porphyroblasts. Staurolite regularly displays multiple growth zones and/or rim overgrowths which together form complex internal structures (Fig. 3A). Growth zones may be inclusion poor or display the internal inclusion fabrics discussed above (Fig. 3A). In addition, some staurolite porphyroblasts exist as shear band boudins and fish (Fig. 3C, D respectively). Staurolite is commonly fractured and displays asymmetrical microboudinage (Figs. 2E, F and 3D). Fractures on which displacement has occurred are typically perpendicular to the long axis (commonly the c-axis) of staurolite grains and generally appear near twin intersections. Optical estimates of the magnitude of relative rotation between most boudinaged staurolite fragments are greater than 20. Boudinaged fragments are commonly separated by mono- to bi-mineralic dilatational

6 Author's personal copy B.M. Frieman et al. / Tectonophysics 587 (2013) Fig. 3. Annotated photomicrographs of Appleton Ridge Formation samples. A) Portion of a staurolite porphyroblast displaying microboudinage, an inclusion rich core, and an inclusion poor rim. B) Staurolite δ-clast displaying dextral shear sense, planar inclusion texture, and a garnet inclusion. C) Staurolite porphyroblast, mantled by matrix biotite, displaying a mica fish microstructure consistent with dextral deformation. D) Shear band crosscutting a boudinaged staurolite porphyroblast with planar inclusion textures. E) Portion of boudinaged andalusite porphyroblast with fibrolitic sillimanite in the boudin neck. F) Syn-kinematic andalusite displaying dextral shear sense and continuity between the inclusion and matrix fabrics. Dotted lines trace foliation or inclusion trails. And = andalusite, Bt = biotite, Grt = garnet, Ms = muscovite, St = staurolite, Qz = quartz. zones that are composed of quartz± feldspar and display grain sizes larger than those of the matrix (Figs. 3B, D, E, 4 and 5A, B, C, D, E) Relative timing of D3 deformation and metamorphism The latest peak regional metamorphic grade attained intermediate amphibolite facies at low pressure high temperature conditions and is defined by the occurrence of staurolite, garnet, and aluminosilicate phases which span the andalusite to sillimanite stability fields (Bickel, 1976; Guidotti, 1989). Staurolite and andalusite grains preserve a relatively complex and protracted history of deformation and mineral growth in their internal growth zoning and inclusion fabrics; however, the latest period records mineral growth during dextral shear deformation. Evidence of this is ubiquitous in the Appleton Ridge Formation and includes synkinematic growth of andalusite and to a lesser extent staurolite (e.g., Fig. 3F). Dilatational zones, which separate boudinaged grains, contain fibrolitic sillimanite (e.g., Fig. 3E), and boudinaged porphyroblasts commonly display necking of the matrix foliation (S3) into interboudin zones (Figs. 3B, D, E, 4 and 5A.1 E.1). The fractures on which boudin separation initiated cross cut all growth zones/

7 68 B.M. Frieman et al. / Tectonophysics 587 (2013) Fig. 4. Criteria used for optical correlation of boudinaged staurolite fragments. (1) Chiefly monomineralic zones between staurolite fragments. Zones exhibit large grain sizes relative to and sharp boundaries with the matrix. (2) Matching fracture patterns at fragment margins. (3) Internal inclusion fabrics (black dotted lines) and/or growth zones. (4) Remnant penetrative twin intersections (outlined in white dotted line). inclusion textures and appear to have largely occurred after the last major period of staurolite growth. These observations suggest that the youngest deformation fabric (i.e. D 3 shear) developed in the Appleton Ridge Formation was synchronous with or slightly postdated the latest phase of regional amphibolite facies metamorphism Methodology of optical microscopy and microstructural analysis Our initial microstructural investigations employed optical analyses of vertical thin sections cut in a series of azimuthal directions relative to an externally fixed geographic reference frame after the method described by Bell et al. (1995). These investigations revealed similar microstructural relationships to those observed in thin sections cut with respect to local fabric orientations in the matrix. For example, serial vertical thin sections displayed staurolite inclusion textures that were rarely continuous with and commonly oblique to matrix fabrics, as well as displaying variable internal fabric orientations among adjacent porphyroblasts (see Section 4.1). Therefore, as our investigation developed, serial vertical thin sections were deemed unnecessary and all the microstructural observations presented here are from thin sections cut: (a) parallel to the lineation and perpendicular to the foliation, (b) parallel to the lineation and the foliation, or (c) perpendicular to the lineation and the foliation. To establish relative microstructural relationships and assess differential rotations of staurolite porphyroblasts we developed a series of optical criteria for correlating staurolite fragments that had once been part of a single parent grain (Fig. 4): (1) the presence of largely monomineralic zones between staurolite fragments that display grain sizes larger than in the surrounding matrix, exhibit sharp boundaries with the matrix, and may be mantled by necking or inflow textures; (2) geometrical matching of fracture patterns at the boundaries of fragmented staurolite grains; and (3) correlation of internal inclusion and/or growth zoning patterns between fragments. Many samples preserve remnant penetrative twin intersections in one or more of the staurolite fragments that facilitate boudin fragment correlation and, in most cases, represent a relative reference orientation for displaced fragments Electron backscatter diffraction (EBSD) analysis Setup and methodology EBSD analysis was used to determine the crystallographic orientation of staurolite fragments in three dimensions; with these data, we measured the relative rotation of staurolite fragments that had originally been part of a single parent grain. We selected samples for analysis that showed the least evidence for mechanical interaction of separate parent staurolite grains, allowing us to evaluate the relative rotations that occurred due to porphyroblast matrix coupling during D 3 shear. Data collection was carried out on a Tescan Vega II XMU tungsten filament scanning electron microscope at the School of Earth and Climate Sciences Electron Microscopy Lab, University of Maine. All analyses were on manually polished and uncoated thin sections under the following physical parameters: high vacuum (~2e-3 Pa), operating voltage= 20 kv, tilt=70, probe current=3 5 na, working distance=25 mm. Indexing of the staurolite crystals was carried out using a structure file built for this study based on lattice distributions and site populations from Hawthorne et al. (1993) using a pseudo-orthorhombic/ monoclinic symmetry (C2/m; α=γ=90.0, β=90.1 ). Bands used for indexing were optimized and refined using >60 unique electron backscatter diffraction patterns of staurolite. The resultant structure file was then tested using a polished crystal stub of known orientation (c-axis reference). Full-section and selected area scans were collected and processed using EDAX-TSL OIM Data Collection and Analysis version 5.3 software. Data processing and management involved one or more of the following: a minimum Confidence Index condition of 0.05, pseudo-symmetry corrections about the major crystallographic axes (e.g., 180 about {100}, {010} and {001}), a minimum grain size requirement of 2 3 times the scan step size (typically μmstepsize),anda neighbor orientation correlation routine. Confidence Index (CI) is a parameter used by the OIM software to rank all possible diffraction pattern solutions relative to one another. This is accomplished by a voting scheme that compares each pattern solution to the next best fit, thereby quantitatively ranking all possible diffraction pattern solutions. Using CI, a neighbor orientation correlation routine may be preformed to reduce data noise, in the form of random misindexing, by modifying the crystallographic orientation of a data point that is below a user

8 B.M. Frieman et al. / Tectonophysics 587 (2013) defined minimum CI to the orientation of the highest CI data point that is in direct contact. Resulting orientation maps were reduced to an average orientation per grain and plotted on pole figures as equal-area, lower-hemisphere projections using a software program developed by Mainprice (1990) (PF_Euler_PC, available online at ftp:// EBSD results The results of our EBSD analysis provided the relative crystallographic orientation of staurolite fragments as well as the relative rotation axes and magnitudes of rotation (Figs. 5 and 6). Every staurolite fragment for which we determined a unique crystallographic orientation was given a letter designation. All fragments display rotation of the principal crystallographic axes relative to a parent orientation; however, the magnitude of relative rotation of any given crystallographic axis varies considerably from sample to sample (Figs. 5 and 6). The magnitudes of rotation (i.e. the misorientation angles) are calculated as the minimum amount of rotation necessary to make the fragment orientation coincident with the reference parent orientation (Fig. 6A). We report the axes necessary to achieve that rotation (Fig. 6B) in a crystallographic reference frame. All samples display remnant penetrative twin intersections at 60 or 90 preserved within one or more of the boudinaged staurolite fragments (twin relationship indicated by * in Fig. 6A). The remnant twin orientations in most cases represent a local reference orientation that, in part, facilitated correlation among the fragments and provided an indication of the initial grain shapes and orientations of formerly contiguous twinned staurolite grains prior to disaggregation and relative rotation during the non-coaxial D 3 event. Relative rotation magnitudes range from 15 to 63 (Fig. 6A) with an average magnitude across all fragments analyzed of 35. In some cases the axial orientation data exhibit apparent curvilinear trends (e.g., Fig. 5A.2 B.2, and E.2a). However, the axial orientation data for the remaining samples display no clear trend (e.g., Fig. 5C.2 and E.2b). Furthermore, the relative rotation axes are generally not coincident both within and between samples and individual boudin fragments consistently yield unique rotation axes out of the shear plane (Fig. 6B). 5. Discussion and implications of microstructural analysis 5.1. Discussion of electron backscatter diffraction (EBSD) results The results of the EBSD analysis (Figs. 5, 6) describe the relative crystallographic orientation of microboudinaged staurolite grains that were formerly contiguous crystals prior to a period of dextral shearing at synto post-peak amphibolite facies conditions. In this section, we consider the factors that control rotation amounts and axes, including the initial grain orientation and shape, the shape of fragmented grains that developed as boudinage progressed, flow perturbation due to fragment proximity, and the degree of fragment matrix coupling. Sample-to-sample differences in the magnitude and style of rotation likely resulted in part from differences in the initial orientation of staurolite crystals relative to the D 3 kinematic reference frame. Based on numerous outcrop to thin-section scale observations and the EBSD results, we propose the conceptual relationships compiled in Fig. 7. For example, sample 10S (Fig. 5.E) preserves a near complete symmetric staurolite twin, which displays significantly different fragment morphologies and rotational trends by each of the conjugate twins (Fig. 5E.2a, b). Specifically, the rotation of fragments F and G,fromsample10S,werelargely accommodated by the a- and b-axes with little change c-axis orientations (Fig. 5E.2b). In contrast, fragments A, B, C, and E display near equal magnitudes of rotation by all three crystallographic axes (Fig. 5E.2a). More generally, we know that the rotational behavior of a rigid particle embedded in a viscously deforming matrix is controlled by the triaxial aspect ratio of the particle and its orientation relative to the kinematics of interest (Ghosh and Ramberg, 1976; Jeffery, 1922). Recent studies have emphasized the importance of clast shape in three dimensions and how this variation can lead to erroneous results when traditional kinematic vorticity gauges are applied (e.g., Li and Jiang, 2011). In addition, we expect added complexity to arise from the perturbation of matrix flow around complex rigid particle shapes (e.g., staurolite crosses) and due to the presence of weak zones (e.g., mica-rich domains), which can lead to local variations in the spatial distribution of vorticity and affect the rotation of nearby clasts (Ildefonse et al., 1992; Jessell et al., 2009; Johnson et al., 2009a,b; Mandal et al., 2005). We interpret our results to be representative of these types of complexity such that staurolite fragments in the Appleton Ridge Formation display variable amounts of rotation out of the shear plane and yield inconsistent inter- and intra-sample rotational behavior (e.g., Figs. 5 and 7). Therefore any measurements made in the standard kinematic reference frame would underestimate the shear strain and/or mean kinematic vorticity number. Despite the quantitative challenges, we observe 3D rotational trends and microstructures qualitatively consistent with the bulk kinematics Geologic implications A number of studies in recent years have investigated the orientation of internal inclusion trails and their geometric relationships (e.g., Foliation Intersection Axes; FIAs) to infer the geometric evolution of multiple deformed regions and infer the overriding plate scale kinematics or boundary conditions (Bell and Welch, 2002; Bell et al., 1995; Cihan, 2004; Sanislav, 2011; Yeh, 2007). These investigations assume that porphyroblasts do not rotate relative to one another or an external reference frame, thereby preserving geometrical relations arising from different deformation events. These studies typically yield data sets that are consistent over a wide range of scales from outcrop (Aerden et al., 2010; Jung et al., 1999) totensorhundredsof square kilometers (Aerden, 1995; Fyson, 1980; Ilg and Karlstrom, 2000; Johnson, 1992; Yeh, 2007). However, as noted by Johnson et al. (2006) and Johnson (2009), the range of inclusion-trail orientations in individual samples is typically These large sample-scale variations have been explained as preservation of local foliation variations (Bell et al., 1992), variable rotation of porphyroblasts with differing shapes and/or orientations (Johnson, 2009; Johnson et al., 2006; Passchier et al., 1992), rigid object interactions (Ildefonse et al., 1992; Jessell et al., 2009; Piazolo et al., 2002), differential timing of porphyroblast growth (Bell et al., 1995), and heterogeneous distributions of strain at the thin section scale (Paterson and Vernon, 2001). Furthermore, these data sets generally provide equivocal evidence for addressing the question of whether or not porphyroblasts rotate relative to one another. In order to unequivocally address this question, the original relative orientations of porphyroblasts and/or their internal inclusion trails must be known. Where relative orientations can be constrained, there is unequivocal evidence that porphyroblasts can and do rotate relative to one another during deformation (Johnson et al., 2006; Johnson, 2009; thisstudy). The basis for using inclusion-trail orientation data as discussed above is rooted in the idea that to maintain space and boundary continuity during bulk inhomogeneous deformation of heterogeneous earth materials strain fields develop which favor mineral redistribution and fabric development, which in turn results in partitioning of the bulk flow into discrete domains of pure and simple shear (e.g., Bell, 1981, 1985). In the Appleton Ridge Formation, anastamosing networks of interconnected mica and shear bands are ubiquitously developed, and it is likely that these fabrics facilitated the localization of shear strain. If so, porphyroblasts in these rocks may record relatively little rotation in comparison to the bulk shear strain (e.g., Bell, 1981, 1985; Fay et al., 2008; Griera et al., 2011; Johnson et al., 2009a,b; ten Grotenhuis et al., 2002).

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10 B.M. Frieman et al. / Tectonophysics 587 (2013) Fig. 5. Staurolite fragment orientations from the five analyzed samples (A E). For each sample: (1) Backscattered electron images with staurolite microstructures of interest outlined and fragments identified by letters. (2) Equal-area, lower-hemisphere projections of staurolite crystallographic axes; letters refer to the fragments in (1). (3) Graphical representation of fragment orientations; shear sense indicated in upper right. Many workers have suggested that boundaries between large, rigid grains (i.e. porphyroblasts or porphyroclasts) and the surrounding matrix may be partially to completely lined by low viscosity material such as molecular water, fine grained recrystallized grains, and/or micaceous minerals, and that these lubricated interfaces may have a profound effect on partitioning of strain, clast matrix shear stress coupling, spatial vorticity distributions, and thus the rotational behavior of these grains (e.g., Ceriani et al., 2003; Ildefonse and Mancktelow, 1993; Jiang and Williams, 2004; Johnson, 1990; Johnson et al., 2006, 2009a,b; Mancktelow et al., 2002; Marques et al., 2005; Mulchrone, 2007; Passchier and Simpson, 1986; Pennacchioni et al., 2001; ten Grotenhuis et al., 2002). Furthermore, partitioning due to the presence of these heterogeneities may explain why rigid clast vorticity gauges (e.g., Passchier, 1987) commonly yield

11 72 B.M. Frieman et al. / Tectonophysics 587 (2013) Fig. 6. (A) Misorientation angles and (B) rotation axes of boudin fragments relative to local reference orientations (marked in brackets). Misorientation angles are the minimum magnitude of rotation. lower mean kinematic vorticity numbers when compared to alternative matrix based methods, such as oblique grain shape or quartz c-axis fabrics (e.g., Bailey and Eyster, 2003; Jessup et al., 2006; Johnson et al., 2009a,b; Law et al., 2004; Sullivan, 2008; Wallis, 1995; Xypolias, 2009, 2010; Xypolias and Kokkalas, 2006). The microboudinage and rotation of staurolite porphyroblasts documented above require shear coupling at the matrix porphyroblast margin. Thus, despite the presence of mineralogically segregated layering in the matrix (e.g., a spaced schistosity) that may facilitate strain partitioning, there is still effective porphyroblast matrix shear coupling. Less clear is how these microstructural variations affect partitioning of kinematic parameters (e.g., shear strain rate and vorticity). Several previous studies have focused on the specific role of clast matrix boundary lubrication (as discussed above) and thus limited their analyses to relatively low viscosity heterogeneities directly adjacent to rigid clasts (Jiang and Williams, 2004; Johnson, 2008) or fully enveloping them Fig. 7. Schematic representation of the effect of porphyroblast orientation and boudin shape on rotations. (A) Untwinned staurolite specimens that are initially parallel or perpendicular to the stretching direction. Asymmetric microboudinage occurs only in the lineation-parallel porphyroblast. (B) Penetrative twin oriented with one of the twin's c-axes at a high angle to the foliation plane; note the tiling of boudinaged fragments. (C) Penetrative twin oriented with both c-axes subparallel to the foliation plane. (D) Penetrative twin with both c-axes oblique to the foliation and lineation. (E) Kinematics used in these representations.

12 B.M. Frieman et al. / Tectonophysics 587 (2013) (Ceriani et al., 2003; Jiang and Williams, 2004; Johnson et al., 2009a,b; Mancktelow et al., 2002; Pennacchioni et al., 2001; Schmid and Podladchikov, 2005). In these cases it has been shown that, in part, the stable orientation, aspect ratio, and rotation rate of rigid clasts may be sensitive to the thickness, morphology, and relative viscosity of inclusion matrix boundary heterogeneities (Jiang and Williams, 2004; Johnson et al., 2009a,b; Schmid and Podladchikov, 2005). In the next section, we evaluate the influence of additional parameters, namely the relative distance and strength contrast between low-viscosity domains and the strong inclusion. 6. Finite element numerical modeling 6.1. Setup and method It is difficult from direct measurements and observations of Appleton Ridge Formation samples to assess the degree to which (1) porphyroblast matrix coupling occurred, (2) porphyroblast kinematics may be affected by the location of weak domains, and (3) how microstructural and rheological heterogeneity affect bulk rock strength. To address these questions we have constructed synthetic microstructures (see Fig. 8A) containing a relatively large central rigid inclusion of fixed dimensionless viscosity (η clast =10 3 ) intended to simulate a subspherical porphyroblast. We limited this investigation to subspherical inclusion shapes in order to eliminate the effects of particle shape and/or initial orientation. The rigid inclusion is embedded in a homogeneous matrix with an isotropic, dimensionless viscosity (η matrix =1) that is intended to simulate a simple quartzofeldspathic background matrix. Two subplanar domains are placed above and below the rigid inclusion to simulate the presence of a material that is weak in shear, such as mica. The spatial distribution and dimensionless viscosity of the weak domains are then varied (Fig. 8A). We performed a large number of experiments simulating a range of common layered or sub-planar structures at various modal concentrations and those presented below are considered to be representative of the general trends that we observed. We employed the finite element numerical method of Gerbi et al. (2010), which is briefly reviewed below (Fig. 8B) and is similar to a number of other comparable investigations (e.g., Biermeier et al., 2001; Bons et al., 1997; Johnson, 2008; Tenczer et al., 2001). The numerical portion of this study was restricted to simple shear conditions, which allows for use of the following relationship: τ xy ¼ η b U x y where τ is the shear traction, η b is the bulk viscosity, U is the velocity, and x and y are an orthogonal spatial reference frame. We import a synthetic microstructure into Elle, an open-source microdynamics simulation code (Bons et al., 2008), where each textural domain is assigned a dimensionless viscosity value. The Elle platform is then used to translate the pixel based synthetic microstructure and prescribed domainal viscosity values into a form that can be used by Basil, a finite element code for 2D incompressible viscous deformation (Barr and Houseman, 1996; Houseman et al., 2008). In Basil, the geometry is subjected to a boundary velocity which corresponds to a shear gradient of unity and results in the following simplification of Eq. (1):if U x / y=1 and U is dimensionless, then τ xy is numerically equivalent to η b. This simplification allows for the calculation of an instantaneous bulk effective viscosity for a given synthetic microstructure. For truly isotropic domains the shear traction calculated for the top and bottom boundaries should be identical. Our models typically yield shear traction values for the top and bottom boundaries that differ by 1 3%, and we use the average of the two. Results from this method have been benchmarked against theoretical and analytical solutions for viscous strength (Gerbi, 2012; Gerbi et al., 2010). We are interested in obtaining the effective bulk viscosity and instantaneous distribution of kinematic parameters for a given synthetic microstructure, as opposed to investigating the fabric evolution; thus the models were run for only a single time step. The calculations assume that the constituent phases behave as linear viscous materials. We justify this assumption for our purposes because: (1) the model runs for a single time step for which an effective viscosity may always be calculated, (2) we are not evaluating strain-rate dependence or the textural evolution, and (3) use of a power law matrix does not substantially affect the first-order rotational behavior of rigid circular inclusions (cf. Bons et al., 1997). ð1þ Fig. 8. (A) Schematic representation of geometries and dimensionless viscosity distributions used in the sensitivity analysis. Inclusion and matrix viscosities (η) are fixed for all model runs at 10 3 and 1 respectively, while the spatial distribution and viscosity of the weak layers are varied from one experiment to another. (B) Geometric representation of dimensionless bulk effective viscosity calculation method. Dark gray square represents the initial geometry. Synthetic microstructures are mapped in this geometry which is then sheared at a prescribed velocity gradient. Model output includes the shear traction necessary to perform the deformation. The bulk viscosity is then calculated using Eq. (1). After Gerbi et al., 2010.

13 74 B.M. Frieman et al. / Tectonophysics 587 (2013) Fig. 9. Effective bulk viscosity versus the matrix/weak domain viscosity ratio for Array 1 (A) and Array 2 (B). Each model array consists of three different weak domain distributions: distal, proximal, and intermediate. Vertical gray bar marks the range of viscosity ratios where effective strength equals matrix strength Numerical results In this section we present the results of a sensitivity analysis of two relatively simple model arrays designed to investigate the influence of the spatial proximity and strength of weak layered structures on bulk viscous strength and the domainal distribution of kinematic parameters. For each model array we maintain a constant area fraction of inclusion, weak domain, and matrix material. We then systematically vary the spatial location of the weak domains and for each location we vary the viscosity of the layers from one experiment to another (Fig. 8A). Model Array 1 contains 3.9% weak domain and 4.5% inclusion domain while Model Array 2 contains 5.8% weak domain and 4.5% inclusion domain by area. As constructed, the horizontal length of the weak domains is approximately 57% and 82% of the total model width for Model Arrays 1 and 2 respectively. The remainder of the model geometries in both arrays is made up of a background matrix. For all experimental runs the viscosity of the matrix was fixed at unity and all of the bulk viscosity results are normalized to that value Effective bulk viscosity The results from Array 1 demonstrate that there is a non-linear relationship between the viscosity of the weak domains and the bulk viscosity (Fig. 9A). These results also indicate that the magnitude of bulk weakening depends on the proximity of the weak domains to the central rigid inclusion: the closer the two are together, the weaker the rock. The spread of bulk viscosity values for the different spatial arrangements becomes more pronounced at higher viscosity contrasts between the matrix and weak domains (Fig. 9A). Furthermore, our results indicate that the threshold for bulk weakening (i.e. η b 1) is relatively discrete and occurs at η m /η w depending on the location of weak domains (grayed region of Fig. 9A). The experimental setup for Array 2 was identical to Array 1 except that the area fraction of the weak domains was increased to 5.8%. The results from Array 2 are similar to those in Array 1. Consistent with the larger mode of weak material, bulk strengths in Array 2 are lower than those in Array 1 regardless of the spatial position of the weak domains (Fig. 9). Similar to Array 1, we observe a strong relationship between bulk strength and relative proximity of weak and strong domains in Array 2, with increasing proximity corresponding to a lower aggregate strength (Fig. 9B). However, the relative strength differences between the different textural distributions are less than that observed in Array 1. While, similar to Array 1, the threshold for bulk weakening (i.e. η b 1) is relatively discrete, occurring at η m / η w depending on the location of weak domains (Fig. 9B) Inclusion vorticity For ease of comparison and interrogation, we plot 1-D transects of the magnitude of vorticity through the center of the model geometries (Fig. 10A, C, D, and F). In addition, we show the dimensionless inclusion vorticity versus matrix viscosity ratio for both geometries (Fig. 10B, E). At η m /η w =2 the vorticity recorded within the rigid

14 B.M. Frieman et al. / Tectonophysics 587 (2013) inclusion is minimally reduced and depends on the position of the weak domains in both Arrays (Table 1; Fig. 10B, E). At η m /η w =5 we observe a reduction of the vorticity within the rigid inclusion to near zero values for both Arrays when the weak domains are directly proximal to the inclusion (Table 1; Fig. 10B, E). Both Arrays, however, maintain vortical magnitudes of ~ within the inclusion when the weak domains are in distal or intermediate positions (Table 1; Fig. 10B, D). As we increase the viscosity ratio between matrix domains (e.g., η m /η w ) localization increases as the weak domains accommodate a larger magnitude of the bulk shear component (Fig. 10C, F). The results with η m /η w =10 display an inclusion vorticity of zero when the weak domains are proximal (Fig. 10B). However, at η m /η w =10, both Arrays maintain inclusion vorticity with intermediate or distal weak domains, although the vorticity recorded is ~50 75% of the initial bulk value (i.e. 0.97) and the magnitude of reduction depends on both the mode and location of weak domains (Table 1; Fig. 10B, D). At η m /η w =20 we observe near complete reduction of clast vorticity to zero for all spatial distributions in both model arrays (Table 1; Fig. 10B, D). The exceptions to this observation are both in Array 1, which display an inclusion vorticity of ~0.7 and 0.01 for weak domain distributions that are distal and intermediate respectively (Table 1; Fig. 10B). Model results with matrix viscosity ratios of η m /η w =100 and 200 display vorticity within the inclusions equal to zero; although, in Array 1, relatively large inclusion vorticity is maintained with distal weak domains (Table 1; Fig. 10B). Furthermore, at high matrix/weak viscosity ratios the model results begin to exhibit antithetic velocity cells on the left and right margins of the inclusion; however the magnitude of the velocity in these cells is not sufficient to induce observable antithetic inclusion rotations as shown by Johnson (2008) and Johnson et al. (2009a,b) Discussion of numerical results The results from the effective bulk viscosity calculation indicate that there is a non-linear relationship between the viscosity contrast between matrix domains (e.g., η m /η w ) and the bulk strength. In both model arrays bulk strength depends strongly on the distribution of weak domains relative to a strong inclusion. The relative differences in bulk strength for the various textural distributions are markedly more pronounced at large viscosity contrasts (Fig. 9). Aggregate bulk weakening (i.e. η b 1) displays minimal dependence on the Table 1 Dimensionless inclusion domain vorticity. a η m /η w Array 1 Array 2 Weak domain location Weak domain location Distal Intermediate Proximal Distal Intermediate Proximal b a b Viscosity of background matrix divided by viscosity of weak domains. No solution calculated for prescribed matrix/weak domain viscosity ratio. microstructural configuration and occurs at a relatively well defined threshold in our models (i.e. between η m /η w 2.6 and 5.5). And, although bulk weakening occurs at those low viscosity ratios, we continue to document vorticity in the rigid inclusion until η m /η w = 5 20 depending on the location of weak domains (see Table 1; Fig. 10B, C, E, F). This indicates that the bulk strength of rocks bearing strong, rigid inclusions is more sensitive to the presence of microstructural and rheological heterogeneities than is the kinematic behavior of these inclusions. Therefore, in general, bulk weakening does not equate to kinematic decoupling. Prior investigations have indicated that the thickness and morphology of proximal low viscosity heterogeneities around rigid inclusions can lead to reduced rotation rates, rotations antithetic to the shear sense, and stable clast orientations not predicted by the traditional theoretical formulations (see Section 4.2; Jiang and Williams, 2004; Johnson et al., 2009a,b; Schmid and Podladchikov, 2005 and references therein). Our results support these conclusions and suggest that direct contact of rheologically weak domains is not required to perturb ideal clast matrix coupling relationships and thereby alter the vorticity partitioned into rigid inclusions. Furthermore, relatively minor microstructural variations can result in significantly different bulk strengths. Many studies suggest that rigid inclusions embedded in a viscous material respond relatively quickly to any applied torque and therefore provide an accurate measure of the instantaneous flow kinematics (Jiang and Williams, 2004; Law, 2010; Xypolias, 2009). However as shown here, the magnitude of vorticity transmitted across the rigid inclusion matrix interface may be significantly perturbed by rheological heterogeneities in the matrix. This dependence may explain why clast-based vorticity gauges commonly yield lower mean kinematic vorticity numbers then that measured by matrix-based gauges in the same rocks (e.g., Bailey and Eyster, 2003; Jessup et al., 2006; Johnson et al., 2009a,b; Law et al., 2004; Sullivan, 2008; Wallis, 1995; Xypolias, 2009; Xypolias and Kokkalas, 2006). For these reasons it may be difficult to use clast-based vorticity gauges to directly infer bulk strain regimes, macroscale kinematics, and the tectonic evolution of metamorphic terranes. Although framed in the context of porphyroblastic schists, our conclusions should apply to any lithology that contains considerable microstructural and rheological heterogeneities. 7. Conclusions We have used microstructural observations, measurements of orientations of previously contiguous staurolite fragments, and numerical calculations of a heterogeneous polyphase composite to conclude the following. (1) The Appleton Ridge Formation preserves a history of boudinage and relative rotation of staurolite porphyroblasts at low to intermediate amphibolite grade due to non-coaxial shear. Staurolite porphyroblast microstructures indicate a protracted history of mineral growth and deformation in their internal inclusion fabrics prior to disaggregation and relative rotation during the youngest phase of deformation. Both porphyroblasts and their internal inclusion fabrics have rotated relative to one another and an externally fixed geographic reference frame, which requires shear coupling at the porphyroblast margins. (2) Rotational behavior of staurolite porphyroblasts in the Appleton Ridge Formation is highly complex in three dimensions and was likely influenced by (a) the initial grain orientation and shape of twinned staurolite porphyroblasts and (b) boudin fragment morphology which evolved as boudinaged progressed. (3) A large portion of the measured staurolite rotation has occurred out of the shear plane and would result in underestimated kinematic vorticity determinations if traditional clast-based vorticity gauges were applied.

15 76 B.M. Frieman et al. / Tectonophysics 587 (2013) Fig. 10. Dimensionless vorticity results for the two Arrays. (A, D) Model geometries displaying the relative distribution of strong and weak domains used in the sensitivity analysis and the location of the 1-D profiles plotted in C and F. (B, E) Plots of the magnitude of dimensionless vorticity recorded in the clast domain versus matrix/weak domain viscosity ratios (ηm/ηw) for the three textural configurations investigated. (C, F) 1-D profiles of the magnitude of dimensionless vorticity versus y-distance through the model geometries at x=0.5.